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Llibres Llibres 101 - 110 de 188 sobre C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides....
" C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. "
A Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of ... - Pągina 66
per Jeremiah Day - 1815 - 126 pągines
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A Treatise on Plane and Spherical Trigonometry

1863 - 256 pągines
...proposition is therefore general in its application.* 118. The »urn of any two side» of a plane triangle ie to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. For, by the preceding article, a : b =»...
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Elements of Plane Trigonometry: And Their Application to the Measurement of ...

1864
...the first proportion in Theorem I. THEOREM III. 41. In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference. Let ABC be a triangle ; then AB + BC:BC—...
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McGill University Calendar, and Examination Papers

1865
...latter formula, determine tan. 15°, first finding tan. 30°. 5. The sum of the two sides of a triangle is to their difference as the tangent of half the sum of the base angles is to the tangent of half the difference. 6. Prove that if A" be the number of seconds...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair, Euclid - 1855 - 317 pągines
...the 3d. Let ABC be a triangle ; the sum of AB and AC any two sides, is to the difference of AB and AC as the tangent of half the sum of the angles ACB and ABC, to the tangent »f half their difference. About the centre A with the radius AB, the greater of the two sides, d«•cribe...
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James Pryde - 1867 - 458 pągines
...the sides a and b and also subtract them, this will give a + b and a — b/ then the sum of the sides is to their difference as the tangent of half the sum of the remaining angles to the tangent of half their difference. The half sum and half difference being added,...
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Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - 1867 - 283 pągines
...sin. B : cos. (AB) ....... (44) THEOREM in. (ART. 9.) In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the ai,(/lei opposite to^them is to the tangent of half then- difference. „ . a sin. A , (Theorem 2.)...
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A TREATISE ON LAND-SURVEYING: COMPRISING THE THEORY DEVELOPED FROM THE ...

W.M. GILLESPIE, L.L. D., CIV. ENG. - 1868
...to each other as the opposite sides. THEOREM II. — In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III.— In every plane triangle,...
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Elements of Trigonometry: Plane and Spherical

Lefébure de Fourcy (M., Louis Etienne) - 1868 - 288 pągines
...tang } (A + B) a — b tang} (A — B) *• ; which shows that, in any triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite to those sides is to the tangent of half their difference. We have A + B=180° — C; hence...
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - 1868 - 420 pągines
...BA-cos. A. That is, b = a cos. C -J- e cos. A. 869. Theorem — The sum of any two sid.es of a triangle is to their difference as the tangent of half the sum of the two opposite angles is to the tangent of half their difference. By Art. 867, a : b : : sin. A : sin....
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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - 1869 - 428 pągines
...to each other at the opposite sides. THEOREM EL — In every plane triangle, the turn of two tides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. — In every plane triangle,...
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